A non-convex framework for structured non-stationary covariance recovery theory and application
Tsai, Katherine
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https://hdl.handle.net/2142/108461
Description
Title
A non-convex framework for structured non-stationary covariance recovery theory and application
Author(s)
Tsai, Katherine
Issue Date
2020-07-09
Director of Research (if dissertation) or Advisor (if thesis)
Koyejo, Oluwasanmi
Department of Study
Electrical & Computer Eng
Discipline
Electrical & Computer Engr
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
machine learning
structured learning
non-convex optimization
non-stationary covariance
dynamic functional connectivity
Abstract
Flexible, yet interpretable, models for the second-order temporal structure are
needed in scientific analyses of high-dimensional data. The thesis develops a
structured time-indexed covariance model for non-stationary time-series data
by decomposing them into sparse spatial and temporally smooth components.
Traditionally, time-indexed covariance models without structure require a large
sample size to be estimable. While the covariances factorization results in both
domain interpretability and ease of estimation from the statistical perspective,
the resulting optimization problem used to estimate the model components
is non-convex. We design an optimization scheme with a carefully tailored
spectral initialization, combined with iteratively re ned alternating projected
gradient descent. We prove a linear convergence rate for the proposed descent
scheme and establish sample complexity guarantees for the estimator. As a
motivating example, we consider the neuroscience application of estimation of
dynamic brain connectivity. Empirical results using simulated and real brain
imaging data illustrate that our approach improves time-varying covariance
estimation as compared to baselines.
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